一类含BESSEL函数无穷积分的一致有界性

Uniform Boundedness of a Class of Infinite Integrals of Bessel Functions

本文讨论了无穷积分integral from n=0 to r|J_n(r)|~qdr的一致有界性,证明存在常数C_2>C_1>0使当q→4^+时,有C_1/(q-4)≤sup integral from n=0 to ∞ r|J_n(r)|~qdr≤C_2/(q-4)。

In this paper, we consider infinite integrals .integral from n=0 to ∞r|J_n(r)|~qdr for 4<q<∞, we prove the following results: Theorem: There exist two constants C_2>C_1>0, such that: C_1~q/(q-4) ≤■integral from n=0 to ∞ o r|J_n(r)|~qdr≤(C_2(q-2)/(q-4)^(q-2)/2 for every 4<q<∞. Where N is the set of all nonnegative integrals. Corollary: If 4<M<∞, then there exist two constants C_2>C_1>0, such that: C_1/(q-4)≤■integral from n=0 to ∞r|J_n(r)|~qdr≤C_2/(q-4·